Page 736 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Biological Reactions and Kinetics 691

m
u (358C) 4 day, while for design, the suggested mean cell a carbon source, as abstracted from Rittman and McCarty
c
residence time for a reactor is u c (358C) 10 day (Tchobano- (2001, p. 143), using half-reactions as given in their tables,
glous and Burton, 1991, p. 818), which apply to ‘‘complete-

þ
mix’’ digesters. In practice, 20 < u c (358C) < 30 day, which f e R a :0.45 [1=5NO 3 þ 6=5H þ e ! 1=10N 2 þ 3=5H 2 O]
allows for uncertainty in the process, such as the high sensi- f s R c : 0.55 [1=28NO 3 þ 5=28CO 2 þ 29=28H þ e

þ
tivity of the methane-former bacteria to environmental condi- ! 1=28C 5 H 7 O 2 N þ 11=28H 2 O]
tions. The most common application of anaerobic treatment is
R d : 1=30C 6 H 5 COO þ 13=30H 2 O

for municipal sludge stabilization, which is a traditional term
! 1=5CO 2 þ 1=30HCO 3 þ H þ e :

þ

that refers to the completion of an anaerobic reaction to the
extent that the substrate is no longer noxious. In fact, the R: 0.0333C 6 H 5 COO þ 0.1096NO 3 þ 0.1096H þ

sludge from the underflow of a primary settler, a highly
! 0.0196C 5 H 7 O 2 N þ 0.045N 2 þ 0.0333HCO 3
objectionable substance that does not dewater significantly,
þ 0.1018CO 2 þ 0.0528H 2 O
becomes after anaerobic digestion, a different material that
has a musty, earthy odor and that dewaters easily in ‘‘sludge- As seen, the half-reactions are each for one electron-equiva-
drying beds.’’ Also, it is easily worked into soil for agricul- lent (e-eq), and the addition of the three half-reactions must
tural disposal (subject to regulations). result in zero electrons for the final equation, R. The coeffi-
cients in the final equation, R, are mol of each reactant and
22.3.3.5 Balancing Equations by Half-Reactions product for an electron-equivalent (since the overall equation
The stoichiometry of any redox reaction can be determined by balance is based upon zero resultant electrons). The final
the technique of adding ‘‘half-reactions’’ (see Section equation can be ‘‘normalized’’ about any reactant or any
20.2.1.3). Tables of half-reactions, as in Table 20.1, are product by dividing by the respective coefficient. For
given in handbooks such as Latimer (1952), and Lide (1996, example, to normalize about benzoate, divide the whole
pp. 8-20–8-29). The technique is described in chemistry texts equation by 0.0333. The resultant equation also gives the
(e.g., Silberberg, 1996, p. 159) and is based on the principle stoichiometric requirements for the reaction (2.63 kg
that the electron balance is zero when oxidation and reduction benzoate=kg NO 3 as N),

half-reactions are added to obtain an overall reaction. The X=(0.0333 mol benzoate 121 g benzoate=mol benzoate) ¼
method is addressed here as an introduction and does not 1g NO 3 as N=(0.1096 mol N 14 NO 3 as N=mol N)

provide sufficient detail for an operational capability.
The half-reaction method applied to biochemical reactions X ¼ 2:63 kg benzoate= kg NO as N

3
was started by Professor Perry L. McCarty (e.g., McCarty,
1965, 1975; Christensen and McCarty, 1975) and is summar- 22.3.3.5.1 Calculation of f s and f e : Synopsis
ized in texts, e.g., Orhon and Artan (1994, pp. 86–107) and
In the foregoing example, the fraction split between f s and f e
Rittman and McCarty (2001, pp. 132–161). The summary that was assumed (keeping in mind that f s þ f e ¼ 1). Actually, how-
follows was abstracted mostly from Rittman and McCarty ever, the fractions used for synthesis and energy, f s and f e , are
(2001, pp. 132–161), which also provides representative unknown, but can be determined as described by Rittman and
half-reactions, R a for the electron acceptors, R c for cell syn- McCarty (2001, pp. 154–161). In their method, the free energy
thesis, R d for the electron donors. An overall reaction is given of the electron donor (e.g., glucose) oxidation, DG r , is deter-
as (Rittman and McCarty, 2001, p. 143), mined from tabular data. The value of DG s is the DG from the
electron donor half-reaction (benzoate to pyruvate) and the DG
(22:15)
R ¼ (1 f s )R a þ f s R c R d of the cell synthesis reaction (obtained from available data and
an empirical relation, respectively); each of the latter is divided
where by a factor, e, which is an efficiency factor for the respective
R is the overall reaction, written on an electron equivalent energy conversions. From this a factor, A, is calculated, which
basis (e-eq.) is the fraction of electron donor that must be oxidized to
R a is the half-reaction for electron acceptor, e.g., oxygen, provide the free energy to synthesize one equivalent of cells,
nitrate, etc. DG s . The two factors, e, which is assumed and A, which is
R c is the half-reaction for cell synthesis, e.g., C 5 H 7 O 2 N calculated, provide a basis for energy accounting, which
R d is the half-reaction for electron donor (the ‘‘substrate’’), is given by Rittman and McCarty (2001, pp. 156) as,
e.g., glucose
f e is the fraction of electron equivalents from electron eADG r þ DG s ¼ 0 (22:16)
donor used for energy,
for which f e ¼ (1 f s ) where
f s is the fraction of electron equivalents from electron
e is an energy transfer efficiency factor where 0.55 e
donor used for cell synthesis 0.70; a typical value is e 0.6 (dimensionless)
A is the fraction of electron donor that must be oxidized to
To illustrate the application of Equation 22.15, the reduction of provide the free energy to synthesize one equivalent of
nitrate to nitrogen gas is shown with benzoate, C 6 H 5 COO ,as cells (dimensionless)